We develop here a spatially resolved, three-dimensional continuum model coupling cluster dynamics (SR-CD) and crystal plasticity to investigate irradiation growth in zirconium. The model uses scale separation to divide the population of the irradiation cluster into mobile and immobile families. Small interstitial and vacancy clusters are modeled using anisotropic reaction–diffusion equations. Among the immobile clusters, an atomistically-informed vacancy cluster to vacancy loop transition is taken into account. The coupling between the evolution equation of CD and the plastic deformation of the material is two-fold, with stress-informed bias factors and local inelastic strains computed from the evolution of the evolving cluster population. The numerical implementation of the model utilizes the finite element method to analyze both single-crystal and polycrystalline samples. The growth strains that are computed align well with the experimental data provided by Carpenter for single-crystal Zr. Furthermore, the transformation of a vacancy cluster into a complete vacancy loop, occurring at a size of 14 nm, is in agreement with experimental observations and atomistic simulations. The density, size, and growth rate of the dislocation loops, denoted as and , also exhibit good agreement with transmission electron microscopy (TEM) analysis of irradiated Zr and its alloys. Our findings demonstrate that there is a spatial correlation between the growth of these dislocation loops and growth strains, significantly influenced by the crystal size. To explain the expansion of the axis and the contraction of the axis in irradiated Zr, it is necessary to consider the diffusion anisotropy difference (DAD) of mobile interstitial species. We show that the PWR Kearns parameters, specifically = 0.63, = 0.32, = 0.05, confer enhanced irradiation resistance to Zr along the principal directions when compared to single crystals. Additionally, reducing the grain size to nanograins further enhances the resistance to irradiation-induced growth, particularly along the direction with the highest volume fraction of basal poles [0001].

中文翻译：

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辐照生长的空间分辨簇动力学模型

我们在这里开发了一个空间分辨的三维连续模型，耦合簇动力学（SR-CD）和晶体塑性来研究锆的辐照生长。该模型利用尺度分离将辐照集群的人口分为流动家庭和固定家庭。使用各向异性反应扩散方程对小型间隙和空位簇进行建模。在不可移动簇中，考虑了原子通知的空位簇到空位循环的转变。 CD 演化方程与材料塑性变形之间的耦合是双重的，其中包含应力信息偏差因子和根据演化簇群的演化计算出的局部非弹性应变。该模型的数值实现利用有限元方法来分析单晶和多晶样品。计算出的生长应变与 Carpenter 提供的单晶 Zr 实验数据非常吻合。此外，空位簇转变为尺寸为 14 nm 的完整空位环，与实验观察和原子模拟一致。位错环的密度、尺寸和生长速率（表示为 和 ）也与辐照 Zr 及其合金的透射电子显微镜 (TEM) 分析表现出良好的一致性。我们的研究结果表明，这些位错环的生长和生长应变之间存在空间相关性，并受到晶体尺寸的显着影响。为了解释Zr辐照下轴的膨胀和轴的收缩，有必要考虑移动间隙物质的扩散各向异性差（DAD）。我们表明，与单晶相比，PWR Kearns 参数（具体为 = 0.63、= 0.32、= 0.05）赋予 Zr 沿主方向增强的耐辐照性。此外，将晶粒尺寸减小为纳米晶粒进一步增强了对辐射诱导生长的抵抗力，特别是沿着基极体积分数最高的方向[0001]。